source: branches/2994-AutoDiffForIntervals/HeuristicLab.Problems.DataAnalysis.Regression.Symbolic.Extensions/ConstrainedConstantOptimizationEvaluator.cs @ 17195

Last change on this file since 17195 was 17195, checked in by gkronber, 6 weeks ago

#2994: added early stopping and fixed a bug in ConstrainedConstantOptimizationEvaluator

File size: 31.2 KB
Line 
1#region License Information
2/* HeuristicLab
3 * Copyright (C) 2002-2019 Heuristic and Evolutionary Algorithms Laboratory (HEAL)
4 *
5 * This file is part of HeuristicLab.
6 *
7 * HeuristicLab is free software: you can redistribute it and/or modify
8 * it under the terms of the GNU General Public License as published by
9 * the Free Software Foundation, either version 3 of the License, or
10 * (at your option) any later version.
11 *
12 * HeuristicLab is distributed in the hope that it will be useful,
13 * but WITHOUT ANY WARRANTY; without even the implied warranty of
14 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
15 * GNU General Public License for more details.
16 *
17 * You should have received a copy of the GNU General Public License
18 * along with HeuristicLab. If not, see <http://www.gnu.org/licenses/>.
19 */
20#endregion
21
22using System;
23using System.Collections.Generic;
24using System.Linq;
25using HeuristicLab.Common;
26using HeuristicLab.Core;
27using HeuristicLab.Data;
28using HeuristicLab.Encodings.SymbolicExpressionTreeEncoding;
29using HeuristicLab.Optimization;
30using HeuristicLab.Parameters;
31using HEAL.Attic;
32
33namespace HeuristicLab.Problems.DataAnalysis.Symbolic.Regression {
34  [Item("Constant Optimization Evaluator (with constraints)", "")]
35  [StorableType("A8958E06-C54A-4193-862E-8315C86EB5C1")]
36  public class ConstrainedConstantOptimizationEvaluator : SymbolicRegressionSingleObjectiveEvaluator {
37    private const string ConstantOptimizationIterationsParameterName = "ConstantOptimizationIterations";
38    private const string ConstantOptimizationImprovementParameterName = "ConstantOptimizationImprovement";
39    private const string ConstantOptimizationProbabilityParameterName = "ConstantOptimizationProbability";
40    private const string ConstantOptimizationRowsPercentageParameterName = "ConstantOptimizationRowsPercentage";
41    private const string UpdateConstantsInTreeParameterName = "UpdateConstantsInSymbolicExpressionTree";
42    private const string UpdateVariableWeightsParameterName = "Update Variable Weights";
43
44    private const string FunctionEvaluationsResultParameterName = "Constants Optimization Function Evaluations";
45    private const string GradientEvaluationsResultParameterName = "Constants Optimization Gradient Evaluations";
46    private const string CountEvaluationsParameterName = "Count Function and Gradient Evaluations";
47
48    public IFixedValueParameter<IntValue> ConstantOptimizationIterationsParameter {
49      get { return (IFixedValueParameter<IntValue>)Parameters[ConstantOptimizationIterationsParameterName]; }
50    }
51    public IFixedValueParameter<DoubleValue> ConstantOptimizationImprovementParameter {
52      get { return (IFixedValueParameter<DoubleValue>)Parameters[ConstantOptimizationImprovementParameterName]; }
53    }
54    public IFixedValueParameter<PercentValue> ConstantOptimizationProbabilityParameter {
55      get { return (IFixedValueParameter<PercentValue>)Parameters[ConstantOptimizationProbabilityParameterName]; }
56    }
57    public IFixedValueParameter<PercentValue> ConstantOptimizationRowsPercentageParameter {
58      get { return (IFixedValueParameter<PercentValue>)Parameters[ConstantOptimizationRowsPercentageParameterName]; }
59    }
60    public IFixedValueParameter<BoolValue> UpdateConstantsInTreeParameter {
61      get { return (IFixedValueParameter<BoolValue>)Parameters[UpdateConstantsInTreeParameterName]; }
62    }
63    public IFixedValueParameter<BoolValue> UpdateVariableWeightsParameter {
64      get { return (IFixedValueParameter<BoolValue>)Parameters[UpdateVariableWeightsParameterName]; }
65    }
66
67    public IResultParameter<IntValue> FunctionEvaluationsResultParameter {
68      get { return (IResultParameter<IntValue>)Parameters[FunctionEvaluationsResultParameterName]; }
69    }
70    public IResultParameter<IntValue> GradientEvaluationsResultParameter {
71      get { return (IResultParameter<IntValue>)Parameters[GradientEvaluationsResultParameterName]; }
72    }
73    public IFixedValueParameter<BoolValue> CountEvaluationsParameter {
74      get { return (IFixedValueParameter<BoolValue>)Parameters[CountEvaluationsParameterName]; }
75    }
76    public IConstrainedValueParameter<StringValue> SolverParameter {
77      get { return (IConstrainedValueParameter<StringValue>)Parameters["Solver"]; }
78    }
79
80
81    public IntValue ConstantOptimizationIterations {
82      get { return ConstantOptimizationIterationsParameter.Value; }
83    }
84    public DoubleValue ConstantOptimizationImprovement {
85      get { return ConstantOptimizationImprovementParameter.Value; }
86    }
87    public PercentValue ConstantOptimizationProbability {
88      get { return ConstantOptimizationProbabilityParameter.Value; }
89    }
90    public PercentValue ConstantOptimizationRowsPercentage {
91      get { return ConstantOptimizationRowsPercentageParameter.Value; }
92    }
93    public bool UpdateConstantsInTree {
94      get { return UpdateConstantsInTreeParameter.Value.Value; }
95      set { UpdateConstantsInTreeParameter.Value.Value = value; }
96    }
97
98    public bool UpdateVariableWeights {
99      get { return UpdateVariableWeightsParameter.Value.Value; }
100      set { UpdateVariableWeightsParameter.Value.Value = value; }
101    }
102
103    public bool CountEvaluations {
104      get { return CountEvaluationsParameter.Value.Value; }
105      set { CountEvaluationsParameter.Value.Value = value; }
106    }
107
108    public string Solver {
109      get { return SolverParameter.Value.Value; }
110    }
111    public override bool Maximization {
112      get { return false; }
113    }
114
115    [StorableConstructor]
116    protected ConstrainedConstantOptimizationEvaluator(StorableConstructorFlag _) : base(_) { }
117    protected ConstrainedConstantOptimizationEvaluator(ConstrainedConstantOptimizationEvaluator original, Cloner cloner)
118      : base(original, cloner) {
119    }
120    public ConstrainedConstantOptimizationEvaluator()
121      : base() {
122      Parameters.Add(new FixedValueParameter<IntValue>(ConstantOptimizationIterationsParameterName, "Determines how many iterations should be calculated while optimizing the constant of a symbolic expression tree (0 indicates other or default stopping criterion).", new IntValue(10)));
123      Parameters.Add(new FixedValueParameter<DoubleValue>(ConstantOptimizationImprovementParameterName, "Determines the relative improvement which must be achieved in the constant optimization to continue with it (0 indicates other or default stopping criterion).", new DoubleValue(0)) { Hidden = true });
124      Parameters.Add(new FixedValueParameter<PercentValue>(ConstantOptimizationProbabilityParameterName, "Determines the probability that the constants are optimized", new PercentValue(1)));
125      Parameters.Add(new FixedValueParameter<PercentValue>(ConstantOptimizationRowsPercentageParameterName, "Determines the percentage of the rows which should be used for constant optimization", new PercentValue(1)));
126      Parameters.Add(new FixedValueParameter<BoolValue>(UpdateConstantsInTreeParameterName, "Determines if the constants in the tree should be overwritten by the optimized constants.", new BoolValue(true)) { Hidden = true });
127      Parameters.Add(new FixedValueParameter<BoolValue>(UpdateVariableWeightsParameterName, "Determines if the variable weights in the tree should be  optimized.", new BoolValue(true)) { Hidden = true });
128
129      Parameters.Add(new FixedValueParameter<BoolValue>(CountEvaluationsParameterName, "Determines if function and gradient evaluation should be counted.", new BoolValue(false)));
130      var validSolvers = new ItemSet<StringValue>(new[] { "non-smooth (minns)", "sequential linear programming (minnlc)" }.Select(s => new StringValue(s).AsReadOnly()));
131      Parameters.Add(new ConstrainedValueParameter<StringValue>("Solver", "The solver algorithm", validSolvers, validSolvers.First()));
132      Parameters.Add(new ResultParameter<IntValue>(FunctionEvaluationsResultParameterName, "The number of function evaluations performed by the constants optimization evaluator", "Results", new IntValue()));
133      Parameters.Add(new ResultParameter<IntValue>(GradientEvaluationsResultParameterName, "The number of gradient evaluations performed by the constants optimization evaluator", "Results", new IntValue()));
134    }
135
136    public override IDeepCloneable Clone(Cloner cloner) {
137      return new ConstrainedConstantOptimizationEvaluator(this, cloner);
138    }
139
140    [StorableHook(HookType.AfterDeserialization)]
141    private void AfterDeserialization() { }
142
143    private static readonly object locker = new object();
144
145    public override IOperation InstrumentedApply() {
146      var solution = SymbolicExpressionTreeParameter.ActualValue;
147      double quality;
148      if (RandomParameter.ActualValue.NextDouble() < ConstantOptimizationProbability.Value) {
149        IEnumerable<int> constantOptimizationRows = GenerateRowsToEvaluate(ConstantOptimizationRowsPercentage.Value);
150        var counter = new EvaluationsCounter();
151        quality = OptimizeConstants(SymbolicDataAnalysisTreeInterpreterParameter.ActualValue, solution, ProblemDataParameter.ActualValue,
152           constantOptimizationRows, ApplyLinearScalingParameter.ActualValue.Value, Solver, ConstantOptimizationIterations.Value, updateVariableWeights: UpdateVariableWeights, lowerEstimationLimit: EstimationLimitsParameter.ActualValue.Lower, upperEstimationLimit: EstimationLimitsParameter.ActualValue.Upper, updateConstantsInTree: UpdateConstantsInTree, counter: counter);
153
154        if (ConstantOptimizationRowsPercentage.Value != RelativeNumberOfEvaluatedSamplesParameter.ActualValue.Value) {
155          throw new NotSupportedException();
156        }
157
158        if (CountEvaluations) {
159          lock (locker) {
160            FunctionEvaluationsResultParameter.ActualValue.Value += counter.FunctionEvaluations;
161            GradientEvaluationsResultParameter.ActualValue.Value += counter.GradientEvaluations;
162          }
163        }
164
165      } else {
166        throw new NotSupportedException();
167      }
168      QualityParameter.ActualValue = new DoubleValue(quality);
169
170      return base.InstrumentedApply();
171    }
172
173    public override double Evaluate(IExecutionContext context, ISymbolicExpressionTree tree, IRegressionProblemData problemData, IEnumerable<int> rows) {
174      SymbolicDataAnalysisTreeInterpreterParameter.ExecutionContext = context;
175      EstimationLimitsParameter.ExecutionContext = context;
176      ApplyLinearScalingParameter.ExecutionContext = context;
177      FunctionEvaluationsResultParameter.ExecutionContext = context;
178      GradientEvaluationsResultParameter.ExecutionContext = context;
179
180      // MSE evaluator is used on purpose instead of the const-opt evaluator,
181      // because Evaluate() is used to get the quality of evolved models on
182      // different partitions of the dataset (e.g., best validation model)
183      double mse = SymbolicRegressionSingleObjectiveMeanSquaredErrorEvaluator.Calculate(SymbolicDataAnalysisTreeInterpreterParameter.ActualValue, tree, double.MinValue, double.MaxValue, problemData, rows, applyLinearScaling: false);
184
185      SymbolicDataAnalysisTreeInterpreterParameter.ExecutionContext = null;
186      EstimationLimitsParameter.ExecutionContext = null;
187      ApplyLinearScalingParameter.ExecutionContext = null;
188      FunctionEvaluationsResultParameter.ExecutionContext = null;
189      GradientEvaluationsResultParameter.ExecutionContext = null;
190
191      return mse;
192    }
193
194    public class EvaluationsCounter {
195      public int FunctionEvaluations = 0;
196      public int GradientEvaluations = 0;
197    }
198
199    private static void GetParameterNodes(ISymbolicExpressionTree tree, out List<ISymbolicExpressionTreeNode> thetaNodes, out List<double> thetaValues) {
200      thetaNodes = new List<ISymbolicExpressionTreeNode>();
201      thetaValues = new List<double>();
202
203      var nodes = tree.IterateNodesPrefix().ToArray();
204      for (int i = 0; i < nodes.Length; ++i) {
205        var node = nodes[i];
206        if (node is VariableTreeNode variableTreeNode) {
207          thetaValues.Add(variableTreeNode.Weight);
208          thetaNodes.Add(node);
209        } else if (node is ConstantTreeNode constantTreeNode) {
210          thetaNodes.Add(node);
211          thetaValues.Add(constantTreeNode.Value);
212        }
213      }
214    }
215
216    public static double OptimizeConstants(ISymbolicDataAnalysisExpressionTreeInterpreter interpreter,
217      ISymbolicExpressionTree tree, IRegressionProblemData problemData, IEnumerable<int> rows, bool applyLinearScaling,
218      string solver,
219      int maxIterations, bool updateVariableWeights = true,
220      double lowerEstimationLimit = double.MinValue, double upperEstimationLimit = double.MaxValue,
221      bool updateConstantsInTree = true, Action<double[], double, object> iterationCallback = null, EvaluationsCounter counter = null) {
222
223      if (!updateVariableWeights) throw new NotSupportedException("not updating variable weights is not supported");
224      if (!updateConstantsInTree) throw new NotSupportedException("not updating tree parameters is not supported");
225      if (!applyLinearScaling) throw new NotSupportedException("application without linear scaling is not supported");
226
227      // we always update constants, so we don't need to calculate initial quality
228      // double originalQuality = SymbolicRegressionSingleObjectiveMeanSquaredErrorEvaluator.Calculate(interpreter, tree, lowerEstimationLimit, upperEstimationLimit, problemData, rows, applyLinearScaling: false);
229
230      if (counter == null) counter = new EvaluationsCounter();
231      var rowEvaluationsCounter = new EvaluationsCounter();
232
233      var intervalConstraints = problemData.IntervalConstraints;
234      var dataIntervals = problemData.VariableRanges.GetIntervals();
235
236      // buffers
237      var target = problemData.TargetVariableTrainingValues.ToArray();
238      var targetStDev = target.StandardDeviationPop();
239      var targetVariance = targetStDev * targetStDev;
240      var targetMean = target.Average();
241      var pred = interpreter.GetSymbolicExpressionTreeValues(tree, problemData.Dataset, problemData.TrainingIndices).ToArray();
242      if (pred.Any(pi => double.IsInfinity(pi) || double.IsNaN(pi))) return targetVariance;
243
244      var predStDev = pred.StandardDeviationPop();
245      if (predStDev == 0) return targetVariance; // constant expression
246      var predMean = pred.Average();
247
248      var scalingFactor = targetStDev / predStDev;
249      var offset = targetMean - predMean * scalingFactor;
250
251      ISymbolicExpressionTree scaledTree = null;
252      if (applyLinearScaling) scaledTree = CopyAndScaleTree(tree, scalingFactor, offset);
253
254      // convert constants to variables named theta...
255      var treeForDerivation = ReplaceConstWithVar(scaledTree, out List<string> thetaNames, out List<double> thetaValues); // copies the tree
256
257      // create trees for relevant derivatives
258      Dictionary<string, ISymbolicExpressionTree> derivatives = new Dictionary<string, ISymbolicExpressionTree>();
259      var allThetaNodes = thetaNames.Select(_ => new List<ConstantTreeNode>()).ToArray();
260      var constraintTrees = new List<ISymbolicExpressionTree>();
261      foreach (var constraint in intervalConstraints.Constraints) {
262        if (constraint.IsDerivation) {
263          if (!problemData.AllowedInputVariables.Contains(constraint.Variable))
264            throw new ArgumentException($"Invalid constraint: the variable {constraint.Variable} does not exist in the dataset.");
265          var df = DerivativeCalculator.Derive(treeForDerivation, constraint.Variable);
266
267          // alglib requires constraint expressions of the form c(x) <= 0
268          // -> we make two expressions, one for the lower bound and one for the upper bound
269
270          if (constraint.Interval.UpperBound < double.PositiveInfinity) {
271            var df_smaller_upper = Subtract((ISymbolicExpressionTree)df.Clone(), CreateConstant(constraint.Interval.UpperBound));
272            // convert variables named theta back to constants
273            var df_prepared = ReplaceVarWithConst(df_smaller_upper, thetaNames, thetaValues, allThetaNodes);
274            constraintTrees.Add(df_prepared);
275          }
276          if (constraint.Interval.LowerBound > double.NegativeInfinity) {
277            var df_larger_lower = Subtract(CreateConstant(constraint.Interval.LowerBound), (ISymbolicExpressionTree)df.Clone());
278            // convert variables named theta back to constants
279            var df_prepared = ReplaceVarWithConst(df_larger_lower, thetaNames, thetaValues, allThetaNodes);
280            constraintTrees.Add(df_prepared);
281          }
282        } else {
283          if (constraint.Interval.UpperBound < double.PositiveInfinity) {
284            var f_smaller_upper = Subtract((ISymbolicExpressionTree)treeForDerivation.Clone(), CreateConstant(constraint.Interval.UpperBound));
285            // convert variables named theta back to constants
286            var df_prepared = ReplaceVarWithConst(f_smaller_upper, thetaNames, thetaValues, allThetaNodes);
287            constraintTrees.Add(df_prepared);
288          }
289          if (constraint.Interval.LowerBound > double.NegativeInfinity) {
290            var f_larger_lower = Subtract(CreateConstant(constraint.Interval.LowerBound), (ISymbolicExpressionTree)treeForDerivation.Clone());
291            // convert variables named theta back to constants
292            var df_prepared = ReplaceVarWithConst(f_larger_lower, thetaNames, thetaValues, allThetaNodes);
293            constraintTrees.Add(df_prepared);
294          }
295        }
296      }
297
298      var preparedTree = ReplaceVarWithConst(treeForDerivation, thetaNames, thetaValues, allThetaNodes);
299
300
301      // local function
302      void UpdateThetaValues(double[] theta) {
303        for (int i = 0; i < theta.Length; ++i) {
304          foreach (var constNode in allThetaNodes[i]) constNode.Value = theta[i];
305        }
306      }
307
308      var fi_eval = new double[target.Length];
309      var jac_eval = new double[target.Length, thetaValues.Count];
310
311      // define the callback used by the alglib optimizer
312      // the x argument for this callback represents our theta
313      // local function
314      void calculate_jacobian(double[] x, double[] fi, double[,] jac, object obj) {
315        UpdateThetaValues(x);
316
317        var autoDiffEval = new VectorAutoDiffEvaluator();
318        autoDiffEval.Evaluate(preparedTree, problemData.Dataset, problemData.TrainingIndices.ToArray(),
319          GetParameterNodes(preparedTree, allThetaNodes), fi_eval, jac_eval);
320
321        // calc sum of squared errors and gradient
322        var sse = 0.0;
323        var g = new double[x.Length];
324        for (int i = 0; i < target.Length; i++) {
325          var res = target[i] - fi_eval[i];
326          sse += 0.5 * res * res;
327          for (int j = 0; j < g.Length; j++) {
328            g[j] -= res * jac_eval[i, j];
329          }
330        }
331
332        fi[0] = sse / target.Length;
333        for (int j = 0; j < x.Length; j++) { jac[0, j] = g[j] / target.Length; }
334
335        var intervalEvaluator = new IntervalEvaluator();
336        for (int i = 0; i < constraintTrees.Count; i++) {
337          var interval = intervalEvaluator.Evaluate(constraintTrees[i], dataIntervals, GetParameterNodes(constraintTrees[i], allThetaNodes),
338            out double[] lowerGradient, out double[] upperGradient);
339
340          // we transformed this to a constraint c(x) <= 0, so only the upper bound is relevant for us
341          fi[i + 1] = interval.UpperBound;
342          for (int j = 0; j < x.Length; j++) {
343            jac[i + 1, j] = upperGradient[j];
344          }
345        }
346      }
347
348      if (solver.Contains("minns")) {
349        alglib.minnsstate state;
350        alglib.minnsreport rep;
351        try {
352          alglib.minnscreate(thetaValues.Count, thetaValues.ToArray(), out state);
353          alglib.minnssetbc(state, thetaValues.Select(_ => -10000.0).ToArray(), thetaValues.Select(_ => +10000.0).ToArray());
354          alglib.minnssetcond(state, 0, maxIterations);
355          var s = Enumerable.Repeat(1d, thetaValues.Count).ToArray();  // scale is set to unit scale
356          alglib.minnssetscale(state, s);
357
358          // set non-linear constraints: 0 equality constraints, constraintTrees inequality constraints
359          alglib.minnssetnlc(state, 0, constraintTrees.Count);
360
361          alglib.minnsoptimize(state, calculate_jacobian, null, null);
362          alglib.minnsresults(state, out double[] xOpt, out rep);
363
364
365          // counter.FunctionEvaluations += rep.nfev; TODO
366          counter.GradientEvaluations += rep.nfev;
367
368          if (rep.terminationtype > 0) {
369            // update parameters in tree
370            var pIdx = 0;
371            // here we lose the two last parameters (for linear scaling)
372            foreach (var node in tree.IterateNodesPostfix()) {
373              if (node is ConstantTreeNode constTreeNode) {
374                constTreeNode.Value = xOpt[pIdx++];
375              } else if (node is VariableTreeNode varTreeNode) {
376                varTreeNode.Weight = xOpt[pIdx++];
377              }
378            }
379            // note: we keep the optimized constants even when the tree is worse.
380            // assert that we lose the last two parameters
381            if (pIdx != xOpt.Length - 2) throw new InvalidProgramException();
382          }
383          if (Math.Abs(rep.nlcerr) > 0.01) return targetVariance; // constraints are violated
384        } catch (ArithmeticException) {
385          return targetVariance;
386        } catch (alglib.alglibexception) {
387          // eval MSE of original tree
388          return targetVariance;
389        }
390      } else if (solver.Contains("minnlc")) {
391        alglib.minnlcstate state;
392        alglib.minnlcreport rep;
393        alglib.optguardreport optGuardRep;
394        try {
395          alglib.minnlccreate(thetaValues.Count, thetaValues.ToArray(), out state);
396          alglib.minnlcsetalgoslp(state);        // SLP is more robust but slower
397          alglib.minnlcsetbc(state, thetaValues.Select(_ => -10000.0).ToArray(), thetaValues.Select(_ => +10000.0).ToArray());
398          alglib.minnlcsetcond(state, 0, maxIterations);
399          var s = Enumerable.Repeat(1d, thetaValues.Count).ToArray();  // scale is set to unit scale
400          alglib.minnlcsetscale(state, s);
401
402          // set non-linear constraints: 0 equality constraints, constraintTrees inequality constraints
403          alglib.minnlcsetnlc(state, 0, constraintTrees.Count);
404          alglib.minnlcoptguardsmoothness(state, 1);
405
406          alglib.minnlcoptimize(state, calculate_jacobian, null, null);
407          alglib.minnlcresults(state, out double[] xOpt, out rep);
408          alglib.minnlcoptguardresults(state, out optGuardRep);
409          if (optGuardRep.nonc0suspected) throw new InvalidProgramException("optGuardRep.nonc0suspected");
410          if (optGuardRep.nonc1suspected) {
411            alglib.minnlcoptguardnonc1test1results(state, out alglib.optguardnonc1test1report strrep, out alglib.optguardnonc1test1report lngrep);
412            throw new InvalidProgramException("optGuardRep.nonc1suspected");
413          }
414
415          // counter.FunctionEvaluations += rep.nfev; TODO
416          counter.GradientEvaluations += rep.nfev;
417
418          if (rep.terminationtype != -8) {
419            // update parameters in tree
420            var pIdx = 0;
421            foreach (var node in tree.IterateNodesPostfix()) {
422              if (node is ConstantTreeNode constTreeNode) {
423                constTreeNode.Value = xOpt[pIdx++];
424              } else if (node is VariableTreeNode varTreeNode) {
425                varTreeNode.Weight = xOpt[pIdx++];
426              }
427            }
428            // note: we keep the optimized constants even when the tree is worse.
429            // assert that we lose the last two parameters
430            if (pIdx != xOpt.Length - 2) throw new InvalidProgramException();
431
432          }
433          if (Math.Abs(rep.nlcerr) > 0.01) return targetVariance; // constraints are violated
434
435        } catch (ArithmeticException) {
436          return targetVariance;
437        } catch (alglib.alglibexception) {
438          return targetVariance;
439        }
440      } else {
441        throw new ArgumentException($"Unknown solver {solver}");
442      }
443   
444
445      // evaluate tree with updated constants
446      var residualVariance = SymbolicRegressionSingleObjectiveMeanSquaredErrorEvaluator.Calculate(interpreter, tree, lowerEstimationLimit, upperEstimationLimit, problemData, rows, applyLinearScaling: true);
447      return Math.Min(residualVariance, targetVariance);
448    }
449
450    private static ISymbolicExpressionTree CopyAndScaleTree(ISymbolicExpressionTree tree, double scalingFactor, double offset) {
451      var m = (ISymbolicExpressionTree)tree.Clone();
452
453      var add = MakeNode<Addition>(MakeNode<Multiplication>(m.Root.GetSubtree(0).GetSubtree(0), CreateConstant(scalingFactor)), CreateConstant(offset));
454      m.Root.GetSubtree(0).RemoveSubtree(0);
455      m.Root.GetSubtree(0).AddSubtree(add);
456      return m;
457    }
458
459    #region helper
460    private static ISymbolicExpressionTreeNode[] GetParameterNodes(ISymbolicExpressionTree tree, List<ConstantTreeNode>[] allNodes) {
461      // TODO better solution necessary
462      var treeConstNodes = tree.IterateNodesPostfix().OfType<ConstantTreeNode>().ToArray();
463      var paramNodes = new ISymbolicExpressionTreeNode[allNodes.Length];
464      for (int i = 0; i < paramNodes.Length; i++) {
465        paramNodes[i] = allNodes[i].SingleOrDefault(n => treeConstNodes.Contains(n));
466      }
467      return paramNodes;
468    }
469
470    private static ISymbolicExpressionTree ReplaceVarWithConst(ISymbolicExpressionTree tree, List<string> thetaNames, List<double> thetaValues, List<ConstantTreeNode>[] thetaNodes) {
471      var copy = (ISymbolicExpressionTree)tree.Clone();
472      var nodes = copy.IterateNodesPostfix().ToList();
473      for (int i = 0; i < nodes.Count; i++) {
474        var n = nodes[i] as VariableTreeNode;
475        if (n != null) {
476          var thetaIdx = thetaNames.IndexOf(n.VariableName);
477          if (thetaIdx >= 0) {
478            var parent = n.Parent;
479            if (thetaNodes[thetaIdx].Any()) {
480              // HACK: REUSE CONSTANT TREE NODE IN SEVERAL TREES
481              // we use this trick to allow autodiff over thetas when thetas occurr multiple times in the tree (e.g. in derived trees)
482              var constNode = thetaNodes[thetaIdx].First();
483              var childIdx = parent.IndexOfSubtree(n);
484              parent.RemoveSubtree(childIdx);
485              parent.InsertSubtree(childIdx, constNode);
486            } else {
487              var constNode = (ConstantTreeNode)CreateConstant(thetaValues[thetaIdx]);
488              var childIdx = parent.IndexOfSubtree(n);
489              parent.RemoveSubtree(childIdx);
490              parent.InsertSubtree(childIdx, constNode);
491              thetaNodes[thetaIdx].Add(constNode);
492            }
493          }
494        }
495      }
496      return copy;
497    }
498
499    private static ISymbolicExpressionTree ReplaceConstWithVar(ISymbolicExpressionTree tree, out List<string> thetaNames, out List<double> thetaValues) {
500      thetaNames = new List<string>();
501      thetaValues = new List<double>();
502      var copy = (ISymbolicExpressionTree)tree.Clone();
503      var nodes = copy.IterateNodesPostfix().ToList();
504
505      int n = 1;
506      for (int i = 0; i < nodes.Count; ++i) {
507        var node = nodes[i];
508        if (node is ConstantTreeNode constantTreeNode) {
509          var thetaVar = (VariableTreeNode)new Problems.DataAnalysis.Symbolic.Variable().CreateTreeNode();
510          thetaVar.Weight = 1;
511          thetaVar.VariableName = $"θ{n++}";
512
513          thetaNames.Add(thetaVar.VariableName);
514          thetaValues.Add(constantTreeNode.Value);
515
516          var parent = constantTreeNode.Parent;
517          if (parent != null) {
518            var index = constantTreeNode.Parent.IndexOfSubtree(constantTreeNode);
519            parent.RemoveSubtree(index);
520            parent.InsertSubtree(index, thetaVar);
521          }
522        }
523        if (node is VariableTreeNode varTreeNode) {
524          var thetaVar = (VariableTreeNode)new Problems.DataAnalysis.Symbolic.Variable().CreateTreeNode();
525          thetaVar.Weight = 1;
526          thetaVar.VariableName = $"θ{n++}";
527
528          thetaNames.Add(thetaVar.VariableName);
529          thetaValues.Add(varTreeNode.Weight);
530
531          var parent = varTreeNode.Parent;
532          if (parent != null) {
533            var index = varTreeNode.Parent.IndexOfSubtree(varTreeNode);
534            parent.RemoveSubtree(index);
535            var prodNode = MakeNode<Multiplication>();
536            varTreeNode.Weight = 1.0;
537            prodNode.AddSubtree(varTreeNode);
538            prodNode.AddSubtree(thetaVar);
539            parent.InsertSubtree(index, prodNode);
540          }
541        }
542      }
543      return copy;
544    }
545
546    private static ISymbolicExpressionTreeNode CreateConstant(double value) {
547      var constantNode = (ConstantTreeNode)new Constant().CreateTreeNode();
548      constantNode.Value = value;
549      return constantNode;
550    }
551
552    private static ISymbolicExpressionTree Subtract(ISymbolicExpressionTree t, ISymbolicExpressionTreeNode b) {
553      var sub = MakeNode<Subtraction>(t.Root.GetSubtree(0).GetSubtree(0), b);
554      t.Root.GetSubtree(0).RemoveSubtree(0);
555      t.Root.GetSubtree(0).InsertSubtree(0, sub);
556      return t;
557    }
558    private static ISymbolicExpressionTree Subtract(ISymbolicExpressionTreeNode b, ISymbolicExpressionTree t) {
559      var sub = MakeNode<Subtraction>(b, t.Root.GetSubtree(0).GetSubtree(0));
560      t.Root.GetSubtree(0).RemoveSubtree(0);
561      t.Root.GetSubtree(0).InsertSubtree(0, sub);
562      return t;
563    }
564
565    private static ISymbolicExpressionTreeNode MakeNode<T>(params ISymbolicExpressionTreeNode[] fs) where T : ISymbol, new() {
566      var node = new T().CreateTreeNode();
567      foreach (var f in fs) node.AddSubtree(f);
568      return node;
569    }
570    #endregion
571
572    private static void UpdateConstants(ISymbolicExpressionTreeNode[] nodes, double[] constants) {
573      if (nodes.Length != constants.Length) throw new InvalidOperationException();
574      for (int i = 0; i < nodes.Length; i++) {
575        if (nodes[i] is VariableTreeNode varNode) varNode.Weight = constants[i];
576        else if (nodes[i] is ConstantTreeNode constNode) constNode.Value = constants[i];
577      }
578    }
579
580    private static alglib.ndimensional_fvec CreateFunc(ISymbolicExpressionTree tree, VectorEvaluator eval, ISymbolicExpressionTreeNode[] parameterNodes, IDataset ds, string targetVar, int[] rows) {
581      var y = ds.GetDoubleValues(targetVar, rows).ToArray();
582      return (double[] c, double[] fi, object o) => {
583        UpdateConstants(parameterNodes, c);
584        var pred = eval.Evaluate(tree, ds, rows);
585        for (int i = 0; i < fi.Length; i++)
586          fi[i] = pred[i] - y[i];
587
588        var counter = (EvaluationsCounter)o;
589        counter.FunctionEvaluations++;
590      };
591    }
592
593    private static alglib.ndimensional_jac CreateJac(ISymbolicExpressionTree tree, VectorAutoDiffEvaluator eval, ISymbolicExpressionTreeNode[] parameterNodes, IDataset ds, string targetVar, int[] rows) {
594      var y = ds.GetDoubleValues(targetVar, rows).ToArray();
595      return (double[] c, double[] fi, double[,] jac, object o) => {
596        UpdateConstants(parameterNodes, c);
597        eval.Evaluate(tree, ds, rows, parameterNodes, fi, jac);
598
599        for (int i = 0; i < fi.Length; i++)
600          fi[i] -= y[i];
601
602        var counter = (EvaluationsCounter)o;
603        counter.GradientEvaluations++;
604      };
605    }
606    public static bool CanOptimizeConstants(ISymbolicExpressionTree tree) {
607      return TreeToAutoDiffTermConverter.IsCompatible(tree);
608    }
609  }
610}
Note: See TracBrowser for help on using the repository browser.